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Ponctual electric charge problem

  1. Dec 23, 2008 #1
    Hello everyone, my answer on the following problem is wrong and I don't see why. I am translating the question from another language, I am sorry if the english is not clear.

    Let q1 = 27C localised at x=0, and another charge q2=3C localised at x=1 meters.

    a)Besides infinity, find a point where the net force exerced on a third ponctual charge would be = 0.

    Solution:
    The third charge must be located between q1 and q2 so the forces exerted cancel out.
    If is the distance between q1 and the third charge, then 1-d is the distance between q2 and the third charge. Let qx be the third charge.

    Then by Coulomb's law:
    [tex]0=\frac{kq_{x}q_{1}}{d^{2}}+\frac{kq_{x}q_{2}}{1-d^{2}}[/tex]
    k and qx cancel out, we now have
    [tex]0=27-54d+30d^{2}[/tex]
    This equation has no solution.

    However, if we look at things intuitevely, there must be a point where the forces cancel out. the answer is x=0,750 meters.
    What is wrong?
    Sorry for my english
     
  2. jcsd
  3. Dec 23, 2008 #2

    Doc Al

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    Staff: Mentor

    Two errors here:
    (1) The denominator in the second term should be (1-d)^2, not 1-d^2.
    (2) The sign of the second term must be negative, since the field from q2 points to the left.
     
  4. Dec 23, 2008 #3

    cepheid

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    Staff Emeritus
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    Gold Member

    From your Coulomb equation I get d^2(q2) = -(1 - d^2)q1 = q1d^2 - q1(1m)

    (q2 - q1)d^2 = -q1(1 m)

    -24d^2 = -27(1 m)

    d^2 = 27/24 = 9/8

    d = 3/2*sqrt(2)

    It doesn't match your answer, so maybe I messed up. HOWEVER the point of my post is that, your quadratic equation is clearly wrong. Where did you get the d term from?

    EDIT: Okay, so DocAl pointed out where the mistake was...
     
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